What is the acceleration of these pure rolling rings?

00:46 Hint given | 01:51 Constraint equation | 04:32 Force solution | 08:51 Energy solution | 11:28 Answer

Question GM3L3: Concepts used in solution

F=ma | Constraint equation | Energy conservation | Torque

Problem statement

Two identical rings of mass M and radius R stand on a rough horizontal surface. The rings are in contact at point P. The radius vector to P makes an angle theta with the horizontal as shown in the figure.  A small cylindrical object of mass m is placed symmetrically on the rings at point P and released. It slides on the rings without friction. Find the acceleration of the center of the rings immediately after the release. The rings do not slip on the surface.

How long does it take for a cassette tape to unwind?

00:31 Hint given | 01:00 Solution starts | 02:32 Answer

Question GM1L2: Concepts used in solution

Kinematics

Problem statement

While listening to a cassette, it took time t for the radius of the unwinding tape reel to be reduced by half. How long will it take for the radius to be reduced by a factor of two again?